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Proving 0.999... Is Equal To 1
eldavojohn writes "Some of the juiciest parts of mathematics are the really simple statements that cause one to immediately pause and exclaim 'that can't be right!' But a recent 28 page paper in The Montana Mathematics Enthusiast (PDF) spends a great deal of time fielding questions by researchers who have explored this in depth and this seemingly impossibility is further explored in a brief history by Dev Gualtieri who presents the digit manipulation proof: Let a = 0.999... then we can multiply both sides by ten yielding 10a = 9.999... then subtracting a (which is 0.999...) from both sides we get 10a — a = 9.999... — 0.999... which reduces to 9a = 9 and thus a = 1. Mathematicians as far back as Euler have used various means to prove 0.999... = 1."
Wouldn't 10a (subtract) .999 be exactly 8.991...which breaks the whole "breakthrough"?
Given that 'a' is a known value of .999...
Math...it's so simple, only a mathemtician can't do it.
"both sides we get 10a — a = 9.999... — 0.999... which reduces to 9a = 9 and thus a = 1." But a=.999999......... this is a bit contradictory. I think we need another variable. a!=1 if a already = .999.......
.999 * 10 = 9.99
Whale
You are confusing a symbolic representation for a number because the symbol contains numbers in it.
It is physically impossible to represent certain numbers using base 10. Pi for example. Is is less obvious, but still a fact that 1/3 and 1/9 are in fact impossible to accurately represent using base 10. The .1111... .33333... and .9999... are all of rather limited accuracy symbols, not numbers, just as if I were to say pi = 3.14159+ The 3.14159+ is a symbol representing Pi, not a number, similarly .9999999... is NOT a number, but is instead a symbolic representation of a number.
The fact that long division or electronic calculators come up with those results is an indication of human accounting for the limitations of our mathematical symptoms. Here, try it in a base 8 format.
In base 8, .11111111 = 1/8 + 1/80 + 1/800 ....
That number, multiplied by 7 becomes .77777777777... or 7/8 + 7/80 + 7/800 ... You can use the same bad math you used earlier to prove that 1 = .7777777... base 8 that you used to claim that 1 = .99999 in base 10
But when you translate that back to base 10, you get .111111... base 8 = .140138888.... (base 10). Then base 8 .777777... = base 10 .9809722222222...
As you can quite clearly see that .980972222... is NOT equal to 1
Here, think of it like rabbits. You have 10 crates of rabbits. If the rabbit crates all have 9 male rabbits, you can mulitple 10*9 to get the 90 total rabbits. But if each crate in fact has a 4 male and 5 female rabbits, so that each crate is uncountable (just as the number of 1's in .1111111... can not be counted), then only a moron multiplies 10x9 and expects to get an accurate count of 90 rabbits. Your number is going to be off because male + female rabbits = uncountable, just as .1111111... is uncountable. It is NOT a number.
excitingthingstodo.blogspot.com
This is retarded. 10 x .999 = 9.99... it does not equal 9.999... that example proof in the slashdot post is total bull$h1t!